Assuming you don't get cold easily, you can walk around the indoor areas of the ship in shorts or a wet bathing suit. But, you'll have to divert around open-air areas in all likelihood...a little cold plus the wind will likely make this a little much. You probably won't want this as a general rule onboard because the wind will prohibit you from going out on deck for viewing (or to have the flexibility to do this when you want to or when the ship announces whales off the port side...). We had to bundle up more on the ship than off of it due to the wind.
Check the weather before going, but my staple was jeans and layers on top (t-shirt, 1-2 long sleeve button shirts, 1-2 sweatshirts, fleece jacket, light-weight lined jacket for another layer and wind protection, raingear). 2 pairs of shorts just in case port or landtour is hot (we had incredibly hot weather in the interior and nothing else would have been comfortable). Generally, in port we only needed a t-shirt with a sweat shirt or light jacket coming on and off throughout the day, but we were lucky. No layer is very thick and a single sweatshirt can get some real mileage, so overpacking isn't a problem if you really stick to this philosophy (which I didn't on my first time out) and plan on doing laundry 1 time (which I definitely did). Knit gloves and hat are also probably a good idea for early/late deck viewing and glacier viewing.